I played my 1924 Buescher tuba for years with one of the adapters to standard American shank that Matt Walters used to make. In fact, I think it was the last one of these he made. I still have it, but no longer use it. I was never truly happy with it, no matter what mouthpiece I used. Intonation just wasn't quite right.
Last year I finally replaced the original (European small tuba shank) receiver on it with a standard American one. It probably took me only about a half hour, including making a little "sleeve" to match the OD of the mouthpipe to the ID of the new mouthpiece receiver, and testing and tinkering with the length of that to get the pitch/intonation exactly where I wanted it. This resulted in a surprising and amazing difference, and the horn now plays very well in tune (modulo a couple of minor typical 3-valve tuba issues) and with a great sound. I typically use my Schilke 66 mouthpiece on it now, but am still experimenting now and then with a Miraphone T17 and a Kelly 25. In any event, it's MUCH better than it ever was with any mouthpiece and the adapter, and better than it ever was with any correctly fitting mouthpiece I ever tried in the original small receiver.
There is a lot of "ideology" about what kind of mouthpieces these old Eb tubas with the small receivers "like". My experience has differed from that, although that may be because I wanted a particular "good sound" and sound quality rather than an historically correct result. But I wouldn't know the historically correct result if I heard it, and I doubt that many others would either.
Anyhow ... An adapter is not a long-term way to go with these things. Either find a currently made mouthpiece that works with it for you, have one made that fits it and you like (Doug Elliott would be a good way to go here and probably save you money in the long run), or change out the receiver and see how that works with a mouthpiece with a different shank.
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)